Robust Principal Component Completion
This work addresses foreground extraction and anomaly detection in applications such as video and hyperspectral imaging, representing an incremental improvement over prior RPCA methods.
The paper tackles the mismatch in robust principal component analysis (RPCA) where sparse foregrounds occlude low-rank backgrounds by proposing robust principal component completion (RPCC), which identifies sparse components indirectly through support determination, achieving near-optimal estimates on synthetic data and robust performance on real datasets like color video and hyperspectral data.
Robust principal component analysis (RPCA) seeks a low-rank component and a sparse component from their summation. Yet, in many applications of interest, the sparse foreground actually replaces, or occludes, elements from the low-rank background. To address this mismatch, a new framework is proposed in which the sparse component is identified indirectly through determining its support. This approach, called robust principal component completion (RPCC), is solved via variational Bayesian inference applied to a fully probabilistic Bayesian sparse tensor factorization. Convergence to a hard classifier for the support is shown, thereby eliminating the post-hoc thresholding required of most prior RPCA-driven approaches. Experimental results reveal that the proposed approach delivers near-optimal estimates on synthetic data as well as robust foreground-extraction and anomaly-detection performance on real color video and hyperspectral datasets, respectively. Source implementation and Appendices are available at https://github.com/WongYinJ/BCP-RPCC.